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In this paper, the investigation is first motivated by showing two examples of simple regular symmetrical graphs, which have the same structural parameters, such as average distance, degree distribution and node betweenness centrality, but…
We propose a concept to generate and stabilize diverse partial synchronization patterns (phase clusters) in adaptive networks which are widespread in neuro- and social sciences, as well as biology, engineering, and other disciplines. We…
In this paper, we establish a few new synchronization conditions for complex networks with nonlinear and nonidentical self-dynamics with switching directed communication graphs. In light of the recent works on distributed sub-gradient…
Complex multiplex networks consist of several subnetwork layers, which interact via pairwise inter-layer connections. Relay synchronization between distant layers which are not directly connected, but only via a relay layer, can be observed…
We study the impact of interaction of nodes in a layer of a multiplex network on the dynamical behavior and cluster synchronization of these nodes in other layers. We find that nodes interactions in one layer affects the cluster…
The internal state of a cell in a coupled cell network is often described by an element of a vector space. Synchrony or anti-synchrony occurs when some of the cells are in the same or the opposite state. Subspaces of the state space…
Understanding how the interplay between higher-order and multilayer structures of interconnections influences the synchronization behaviors of dynamical systems is a feasible problem of interest, with possible application in essential…
We study cluster synchronization in networks and show that the stability of all possible cluster synchronization patterns depends on a small set of Lyapunov exponents. Our approach can be applied to clusters corresponding to both orbital…
Natural materials often feature a combination of soft and stiff phases, arranged to achieve excellent mechanical properties, such as high strength and toughness. Many natural materials have even independently evolved to have similar…
It is known that intra-layer adaptive coupling among connected oscillators instigates explosive synchronization (ES) in multilayer networks. Taking an altogether different cue in the present work, we consider inter-layer adaptive coupling…
We explore numerically the synchronization effects in a heterogeneous two-layer network of two-dimensional (2D) lattices of van der Pol oscillators.The inter-layer coupling of the multiplex network has an attractive character. One layer of…
By numerical simulations, we investigate the onset of synchronization of networked phase oscillators under two different weighting schemes. In scheme-I, the link weights are correlated to the product of the degrees of the connected nodes,…
We study optimal synchronization of networks of coupled phase oscillators. We extend previous theory for optimizing the synchronization properties of undirected networks to the important case of directed networks. We derive a generalized…
Symmetries naturally occur in real-world networks and can significantly influence the observed dynamics. For instance, many synchronization patterns result from the underlying network symmetries, and high symmetries are known to increase…
Recent works have highlighted scale invariance or symmetry present in the weight space of a typical deep network and the adverse effect it has on the Euclidean gradient based stochastic gradient descent optimization. In this work, we show…
Adaptation plays a pivotal role in the evolution of natural and artificial complex systems, and in the determination of their functionality. Here, we investigate the impact of adaptive inter-layer processes on intra-layer synchronization in…
A scenario has recently been reported in which in order to stabilize complete synchronization of an oscillator network---a symmetric state---the symmetry of the system itself has to be broken by making the oscillators nonidentical. But how…
This work introduces a methodology for studying synchronization in adaptive networks with heterogeneous plasticity (adaptation) rules. As a paradigmatic model, we consider a network of adaptively coupled phase oscillators with…
We consider anti-phase synchronization of coupled oscillators using the Stuart-Landau model and explore its relative infrequency in occurrence compared to in-phase synchronization. We report effective limits in number of oscillators which…
We show that multiplexing allows to control noise-induced dynamics of multilayer networks in the regime of stochastic resonance. We illustrate this effect on an example of two- and multi-layer networks of bistable overdamped oscillators. In…